As mobile devices become more sophisticated and ubiquitous, airports have greater access to information on the activities of passengers and their reasons for engaging in such activities. This study proposes a novel trajectory-based dynamic choice model that can capture the effects of time stress, store visibility, and trajectory histories on activity choices in airport terminals. To evaluate the proposed model, two surveys on passenger trajectories and activities at Songshan Airport in Taipei, Taiwan, were conducted. The results reveal that although passengers under less time stress are more likely to perform discretionary activities, the dynamics of store-visiting choices suggest that airport shoppers can be distinguished into two types: shoppers whose store-visiting probability is negatively associated with time stress, and shoppers whose store-visiting probability has a concave relationship with time stress. The effect of visual attractiveness is especially strong for process activities (e.g., passing through security screening and passport control), and the variance in the visual-attractiveness effect for discretionary activities (e.g., shopping) is strongly influenced by the airport environment. The results also indicate novelty-seeking behavior: passengers are less likely to do something that they have already done. Our findings suggest that passengers behave heterogeneously in response to various levels of time stress but homogeneously in response to visual cues. Despite the variation in passenger characteristics, this study demonstrates that trajectory data alone are sufficient for the construction of passenger behavior models with satisfactory temporal transferability.